1. Field
The present disclosure relates to the field of communications, and in particular to a method and apparatus for determining a nonlinear characteristic and a system.
2. Description of the Related Art
As continuous increase of a transmission rate of a communication system, much attention is paid to a nonlinear characteristic in the system as it has become one of limiting factors of performance. Among various methods dealing with the nonlinear characteristic in the system, a necessary step is measuring and estimating the nonlinear characteristic so that it can be corrected.
Currently, there are two common methods for measuring and estimating the nonlinear characteristic. One is comparing directly input and output time domain waveforms to obtain an input output transfer function (Document 1), with an advantage of being convenient and direct, and a disadvantage of being large in error for a large bandwidth system, nonlinearity may be under-estimated, and resulting in failure of system transmission. The other one is modeling the nonlinearity of the system first, and then training a model coefficient using a training sequence or an iteration method (Document 2), with an advantage of being more accurate than the first method, and a disadvantage of being complex in the measurement apparatuses and processes, and being hard to meet requirements of a high-speed communication system on hardware and time efficiency.
FIG. 1A is a schematic diagram of a system to be measured with fixed parameters, and FIG. 1B a schematic diagram of a Volterra nonlinear model (referred to as a Volterra model) corresponding to the system to be measured of FIG. 1A. As shown in FIGS. 1A and 1B, in FIG. 1B,
            y      ⁡              (        n        )              =                            ∑                      K            =                                          -                                  (                                                            N                      1                                        -                    1                                    )                                            /              2                                                          (                                                N                  1                                -                1                            )                        /            2                          ⁢                                  ⁢                              h            k                          (              1              )                                ⁢                      x            ⁡                          (                              n                -                k                            )                                          +                        ∑                      k            =                                          -                                  (                                                            N                      2                                        -                    1                                    )                                            /              2                                                          (                                                N                  2                                -                1                            )                        /            2                          ⁢                              ∑                          l              =                                                -                                      (                                                                  N                        2                                            -                      1                                        )                                                  /                2                                                                    (                                                      N                    2                                    -                  1                                )                            /              2                                ⁢                                    h                              k                ,                l                                            (                2                )                                      ⁢                          x              ⁡                              (                                  n                  -                  k                                )                                      ⁢                          x              ⁡                              (                                  n                  -                  l                                )                                                        +                        ∑                      k            =                                          -                                  (                                                            N                      3                                        -                    1                                    )                                            /              2                                                          (                                                N                  3                                -                1                            )                        /            2                          ⁢                              ∑                          l              =                                                -                                      (                                                                  N                        3                                            -                      1                                        )                                                  /                2                                                                    (                                                      N                    3                                    -                  1                                )                            /              2                                ⁢                                    ∑                              m                =                                                      -                                          (                                                                        N                          3                                                -                        1                                            )                                                        /                  2                                                                              (                                                            N                      3                                        -                    1                                    )                                /                2                                      ⁢                                          h                                  k                  ,                  l                  ,                  m                                                  (                  3                  )                                            ⁢                              x                ⁡                                  (                                      n                    -                    k                                    )                                            ⁢                              x                ⁡                                  (                                      n                    -                    l                                    )                                            ⁢                              x                ⁡                                  (                                      n                    -                    m                                    )                                                                        +      …        ⁢          ;where,
      ∑          K      =                        -                      (                                          N                1                            -              1                        )                          /        2                            (                              N            1                    -          1                )            /      2        ⁢          ⁢            h      k              (        1        )              ⁢          x      ⁡              (                  n          -          k                )            is a first-order item, N1 is a memory length, and hk(1) is a coefficient;
      ∑          k      =                        -                      (                                          N                2                            -              1                        )                          /        2                            (                              N            2                    -          1                )            /      2        ⁢            ∑              l        =                              -                          (                                                N                  2                                -                1                            )                                /          2                                      (                                    N              2                        -            1                    )                /        2              ⁢                  h                  k          ,          l                          (          2          )                    ⁢              x        ⁡                  (                      n            -            k                    )                    ⁢              x        ⁡                  (                      n            -            l                    )                    is a second-order item, N2 is a memory length, and hk,l(2) is a coefficient;
      ∑          k      =                        -                      (                                          N                3                            -              1                        )                          /        2                            (                              N            3                    -          1                )            /      2        ⁢            ∑              l        =                              -                          (                                                N                  3                                -                1                            )                                /          2                                      (                                    N              3                        -            1                    )                /        2              ⁢                  ∑                  m          =                                    -                              (                                                      N                    3                                    -                  1                                )                                      /            2                                                (                                          N                3                            -              1                        )                    /          2                    ⁢                        h                      k            ,            l            ,            m                                (            3            )                          ⁢                  x          ⁡                      (                          n              -              k                        )                          ⁢                  x          ⁡                      (                          n              -              l                        )                          ⁢                  x          ⁡                      (                          n              -              m                        )                              is a third-order item, N3 is a memory length, and hk,l,m(3) is a coefficient;n denotes time coordinates of a signal x( ), x(n) is a value of the signal at an n-th moment, x(n+1) is a value of the signal at an (n+1)-th moment, and x(n−k) is a value of the signal at an (n−k)-th moment; and k, l and m denote memory lengths, which are offsets relative to the moment n, for example, x(n) which is offset by a memory length k becomes x(n−k);and so on.
Due to such advantages as the items are complete, the assumptions are few, and accuracy is good, etc., the Volterra model is applicable to estimation of a nonlinear characteristic of a long memory effect of a high-speed large bandwidth.
Document 1: CN103297155A; and
Document 2: Dennis R. Morgan, etc, ‘A Generalized Memory Polynomial Model for Digital Predistortion of RF Power Amplifiers’, IEEE Transactions on Signal Processing, vol. 54, no. 10, 2006.
It should be noted that the above description of the background is merely provided for clear and complete explanation of the present disclosure and for easy understanding by those skilled in the art. And it should not be understood that the above technical solution is known to those skilled in the art as it is described in the background of the present disclosure.